In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel discovered a generalized character theory that proved useful in studying cohomology rings of the form E^*(BG). In this paper we use the geometry of p-divisible groups to describe a sequence of "intermediate" character theories that retain more information about the cohomology theory E and yield the related result of Hopkins, Kuhn, and Ravenel as a special case.